In the mid 1400's, conical shaped spiral pulleys called fusees were first used to improve the accuracy of spring-powered clocks. The fusee converted the linearly increasing torque from a power spring into a constant torque. FIGS. 1a and 1b show two different fusee mechanisms. In both figures, the clock spring is located inside a drum on the left, and the conical fusee is located on the right. A flexible chain connects the drum to the fusee. The drum acts as a constant radius pulley and the fusee acts as a variable radius pulley.
The fusee fell out of favor after the invention of constant force and constant torque springs. The constant torque power springs were no larger than the linear power springs that they replaced. The fusee clocks were larger and they had more moving parts. Constant force and constant torque springs haven't replaced spiral pulleys for all applications. They store less energy per pound and they have a shorter life than other springs. Their force fluctuates slightly as they extend and retract. It's difficult to produce constant force springs with a tight force tolerance. They are not adjustable. In the United States, only a few dozen sizes of constant force springs are available from stock. Other sizes must be custom made.
In addition to the extra parts and space required, spiral pulleys and fusees have other problems. The cables can rub and wear on the sides of the grooves in the fusee. Rubbing occurs when the cable is not tangent to the groove. For example, if the cable approaches the fusee from a nearby idler pulley, the angle between the cable and the groove can be large. This angular error is often called the “fleet angle”. U.S. Pat. No. 5,037,059 discusses one specific solution to this problem.
Spiral pulleys and fusees are poorly understood and difficult to design. The shape and size of a spiral pulley is affected by many parameters. Most patents give only a limited description of their geometry. For example, the 059 patent describes the fusee as “corn shaped”. U.S. Pat. No. 4,685,648 describes the spiral pulley as “irregular” or “snail-shaped”.
FIG. 7 of the 648 patent shows a constant force mechanism with two spiral pulleys. Both the input and the output pulleys are spiral shaped. In other patents and references, only one of the two pulleys has a spiral shape. In FIG. 5, only the input pulley is a spiral. In FIG. 6, only the output pulley is a spiral. The 648 patent does not explain how to determine the shapes that will produce a constant output force.
In FIGS. 2a, b, and c of this patent, prior art pulleys are accurately drawn to show the shapes required to deliver a constant force. In FIGS. 2a and 2c, the input pulleys have a spiral radius as in FIG. 5 of the 648 patent. In FIG. 2b, the output pulley has a spiral radius as in FIG. 6 of the 648 patent. For comparison, each of the figures is drawn to the same scale. Each of the three mechanisms is designed to deliver the same output force Fout and stroke L2.
In FIGS. 2a and 2b, the pulleys have been designed so that the spring extension L1 is equal to the output stroke L2. In FIG. 2c, the pulleys have been designed to minimize the size of the mechanism. The spring extension in FIG. 2c is much smaller than the output stroke. The resulting cable stress is much larger. Compared to the FIGS. 2a and 2b mechanisms, the life and load of the FIG. 2c mechanism is severely limited.